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Journal articles on the topic 'G-stochastic integral'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Guo, C., S. Fang, Y. He, and Y. Zhang. "Stochastic Calculus for Fractional G-Brownian Motion and its Application to Mathematical Finance." Markov Processes And Related Fields, no. 2024 № 4 (30) (February 8, 2025): 477–524. https://doi.org/10.61102/1024-2953-mprf.2024.30.4.002.

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Recently, a new concept for some stochastic process called fractional G-Brownian motion (fGBm) was developed. Compared to the standard Brownian motion, fractional Brownian motion and G-Brownian motion, the fGBm can exhibit long-range dependence and feature volatility uncertainty simultaneously. Thus it generalizes the concepts of the former three processes, and can be a better alternative stochastic process in real applications. In this paper, some stochastic calculus for the fGBm is established and its application to mathematical finance is discussed. First some stochastic integrals with resp

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HERNÁNDEZ, JORGE ELIECER. "ON (m, h1, h2)-G-CONVEX DOMINATED STOCHASTIC PROCESSES." Kragujevac Journal of Mathematics 46, no. 2 (2022): 215–27. http://dx.doi.org/10.46793/kgjmat2202.215h.

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In this paper is introduced the concept of (m, h1, h2)-convexity for stochastic processes dominated by other stochastic processes with the same property, some mean square integral Hermite-Hadamard type inequalities for this kind of generalized convexity are established and from the founded results, other mean square integral inequalities for the classical convex, s-convex in the first and second sense, P-convex and MT-convex stochastic processes are deduced.

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3

El-Sayed, A. M. A., M. Abdurahman, and H. A. Fouad. "Existence and stability results for the integrable solution of a singular stochastic fractional-order integral equation with delay." Journal of Mathematics and Computer Science 33, no. 01 (2023): 17–26. http://dx.doi.org/10.22436/jmcs.033.01.02.

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In this paper, we are concerning with the existence of the solution \( \V \in L_1([0,\tau],L_2(\Omega))\) of the singular stochastic fractional-order integral equation with delay \(\varrho(.) \), \[ \V(t) = B(t) t^{\alpha - 1} + \lambda ~ \I^{\beta} \G(t,\V(\varrho (t))), ~~~t\in (0,\tau], \] where \(B(t)\) is a given second order mean square stochastic process, \( \lambda \) is a parameter, \(\varrho (t) \leq t\), and \(\G(t,\V) \) is a measurable function in \(t \in (0,\tau]\) and satisfies Lipschitz condition on the second argument. %and \(x\in C_{1-\beta}([0,T],L_2(\Omega)) $ will be prove

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4

Choi, Jae. "Conditional wiener integral associated with Gaussian processes and applications." Filomat 37, no. 26 (2023): 8791–811. http://dx.doi.org/10.2298/fil2326791c.

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Let C0[0,T] denote the one-parameter Wiener space and let C?0[0,T] be the Cameron-Martin space in C0[0,T]. Given a function k in C?0[0,T], define a stochastic process Zk : C0[0,T] ? [0, T] ? R by Zk(x, t) = R t 0 Dk(s)dx(s), where Dk ? d/dt k. Let a random vector XG,k : C0[0,T] ? Rn be given by XG,k(x) = ((g1,Zk(x,?))~,..., (gn,Zk(x,?))~), where G = {g1, ..., gn} is an orthonormal set with respect to the weighted inner product induced by the function k on the space C?0[0,T], and (g,Zk(x,?))~ denotes the Paley-Wiener-Zygmund stochastic integral. In this paper, using the reproducing kernel prope

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5

Aoyama, Takahiro, та Makoto Maejima. "Characterizations of subclasses of type G distributions on $ℝ^d$ by stochastic integral representations". Bernoulli 13, № 1 (2007): 148–60. http://dx.doi.org/10.3150/07-bej5136.

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6

Cuong, Dang Kien, Duong Ton Dam, Duong Ton Thai Duong, and Du Thuan Ngo. "Solutions to the jump-diffusion linear stochastic differential equations." Science and Technology Development Journal - Natural Sciences 3, no. 2 (2019): 115–19. http://dx.doi.org/10.32508/stdjns.v3i2.663.

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The jump-diffusion stochastic process is one of the most common forms in reality (such as wave propagation, noise propagation, turbulent flow, etc.), and researchers often refer to them in models of random processes such as Wiener process, Levy process, Ito-Hermite process, in research of G. D. Nunno, B. Oksendal, F. B. Hanson, etc. In our research, we have reviewed and solved three problems: (1) Jump-diffusion process (also known as the Ito-Levy process); (2) Solve the differential equation jump-diffusion random linear, in the case of one-dimensional; (3) Calculate the Wiener-Ito integral to

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7

Ma, Li, and Yujing Li. "Stability Analysis of Stochastic Differential Equation Driven by G-Brownian Motion under Non-Lipschitz Condition." Mathematical Problems in Engineering 2022 (September 1, 2022): 1–16. http://dx.doi.org/10.1155/2022/7592535.

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This paper is devoted to studying the p-th moment exponential stability for a class of stochastic differential equation (SDE) driven by G-Brownian motion under non-Lipschitz condition. The delays considered in this paper are time-varying delays τ i t 1 ≤ i ≤ 3 . Since the coefficients are non-Lipschitz, the normal enlargement on the coefficients is not available and the Gronwall inequality is not suitable in this case. By Bihari inequality and Itô integral formula, it is pointed out that there exists a constant τ ∗ such that the p-th moment exponential stability holds if the time-varying delay

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Noeiaghdam, Samad, and Mohammad Ali Fariborzi Araghi. "A Novel Algorithm to Evaluate Definite Integrals by the Gauss-Legendre Integration Rule Based on the Stochastic Arithmetic: Application in the Model of Osmosis System." Mathematical Modelling of Engineering Problems 7, no. 4 (2020): 577–86. http://dx.doi.org/10.18280/mmep.070410.

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Finding the optimal iteration of Gaussian quadrature rule is one of the important problems in the computational methods. In this study, we apply the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library to find the optimal iteration and optimal approximation of the Gauss-Legendre integration rule (G-LIR). A theorem is proved to show the validation of the presented method based on the concept of the common significant digits. Applying this method, an improper integral in the solution of th

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9

Zhang, Yunlong, Weizhi Xu, Dongsheng Du, and Shuguang Wang. "Stochastic Optimization of Dissipation Structures Based on Lyapunov Differential Equations and the Full Stress Design Method." Buildings 13, no. 3 (2023): 665. http://dx.doi.org/10.3390/buildings13030665.

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This article presents a Lyapunov precise integral-based analysis method for seismic structures with added viscous fluid dampers. This study uses the full stress algorithm as the optimization method, considering the mean square of interstory drifts as the optimization objective, the position of the damper as the optimization object, and the random vibration analysis method as the calculation method to optimize seismic frame structures with viscous dampers. A precise integral solution is derived for the Lyapunov equation based on the general expression of the Lyapunov differential equation for t

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10

Yukich, J. E. "The convolution metric dg." Mathematical Proceedings of the Cambridge Philosophical Society 98, no. 3 (1985): 533–40. http://dx.doi.org/10.1017/s0305004100063738.

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SummaryWe introduce and study a new metric on denned bywhere is the space of probability measures on ℝk and where g: ℝk→ is a probability density satisfying certain mild conditions. The metric dg, relatively easy to compute, is shown to have useful and interesting properties not enjoyed by some other metrics on . In particular, letting pn denote the nth empirical measure for P, it is shown that under appropriate conditions satisfies a compact law of the iterated logarithm, converges in probability to the supremum of a Gaussian process, and has a useful stochastic integral representation.

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11

Bai, Xue-peng, and Yi-qing Lin. "On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients." Acta Mathematicae Applicatae Sinica, English Series 30, no. 3 (2014): 589–610. http://dx.doi.org/10.1007/s10255-014-0405-9.

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Cortés, Juan Carlos, and Marc Jornet. "Lp-Solution to the Random Linear Delay Differential Equation with a Stochastic Forcing Term." Mathematics 8, no. 6 (2020): 1013. http://dx.doi.org/10.3390/math8061013.

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This paper aims at extending a previous contribution dealing with the random autonomous-homogeneous linear differential equation with discrete delay τ > 0 , by adding a random forcing term f ( t ) that varies with time: x ′ ( t ) = a x ( t ) + b x ( t − τ ) + f ( t ) , t ≥ 0 , with initial condition x ( t ) = g ( t ) , − τ ≤ t ≤ 0 . The coefficients a and b are assumed to be random variables, while the forcing term f ( t ) and the initial condition g ( t ) are stochastic processes on their respective time domains. The equation is regarded in the Lebesgue space L p of random variables with f

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13

Tariq, Muhammad, Sher Khan Awan, Asad Ali Chandio, and Imtiaz Ahmad. "A Comprehensive Review Note on Pachpatte-Type Inequality." Global Journal of Sciences 1, no. 1 (2024): 35–39. https://doi.org/10.48165/gjs.2024.1104.

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Convex functions have a long and illustrious history. The history of convexity theory can be traced all the way back to the end of the nineteenth century. The word ”convex functions” has been widely used and explored in the well-known and popular book namely ”Inequalities,” published by G. Polya, G.H. Hardy, and J.E. Littlewood [1]. This book is quickly became a standard reference for mathematicians and dedicated solely to the topic of inequality and serves as an excellent introduction to this fascinating field. Convex theory provides us with appropriate guidelines and techniques to focus on a

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14

KONDRATIEV, YURI G., and EUGENE W. LYTVYNOV. "OPERATORS OF GAMMA WHITE NOISE CALCULUS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 03 (2000): 303–35. http://dx.doi.org/10.1142/s0219025700000236.

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The paper is devoted to the study of Gamma white noise analysis. We define an extended Fock space ℱ ext (ℋ) over ℋ= L2(ℝd, dσ) and show how to include the usual Fock space ℱ(ℋ) in it as a subspace. We introduce in ℱ ext (ℋ) operators a(ξ)=∫ℝddxξ(x)a(x), ξ∈ S, with [Formula: see text], where [Formula: see text] and ∂x are the creation and annihilation operators at x. We show that (a(ξ))ξ∈S is a family of commuting self-adjoint operators in ℱ ext (ℋ) and construct the Fourier transform in generalized joint eigenvectors of this family. This transform is a unitary I between ℱ ext (ℋ) and the L2-sp

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15

Zhang, Xuepeng, Yujing Jiang, Yue Cai, et al. "A Simplified Method for Predicting Tunneling-Induced Ground Movement considering Nonuniform Deformation Boundary." Shock and Vibration 2022 (January 13, 2022): 1–11. http://dx.doi.org/10.1155/2022/6289303.

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Stochastic medium (SM) theory is a practical method in ground settlement prediction, while its nonintegrable double integral form makes the solution process complicated. A simplified analytical solution based on the SM theory is developed to predict the ground movement in tunneling excavation. With the simplified solution, the ground movement for single tunnel and twin tunnels could be predicted based on the gap parameter G and influence angle β. A feasible approach is developed to estimate these two parameters using the maximum ground settlement Smax and tunnel design parameters, including tu

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16

Linetsky, Vadim. "The spectral representation of Bessel processes with constant drift: applications in queueing and finance." Journal of Applied Probability 41, no. 2 (2004): 327–44. http://dx.doi.org/10.1239/jap/1082999069.

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Bessel processes with constant negative drift have recently appeared as heavy-traffic limits in queueing theory. We derive a closed-form expression for the spectral representation of the transition density of the Bessel process of order ν > −1 with constant drift μ ≠ 0. When ν > -½ and μ < 0, the first term of the spectral expansion is the steady-state gamma density corresponding to the zero principal eigenvalue λ0 = 0, followed by an infinite series of terms corresponding to the higher eigenvalues λn, n = 1,2,…, as well as an integral over the continuous spectrum above μ2/2. When −1

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Linetsky, Vadim. "The spectral representation of Bessel processes with constant drift: applications in queueing and finance." Journal of Applied Probability 41, no. 02 (2004): 327–44. http://dx.doi.org/10.1017/s0021900200014339.

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Bessel processes with constant negative drift have recently appeared as heavy-traffic limits in queueing theory. We derive a closed-form expression for the spectral representation of the transition density of the Bessel process of orderν&gt; −1 with constant driftμ≠ 0. Whenν&gt; -½ andμ&lt; 0, the first term of the spectral expansion is the steady-state gamma density corresponding to the zero principal eigenvalueλ0= 0, followed by an infinite series of terms corresponding to the higher eigenvaluesλn,n= 1,2,…, as well as an integral over the continuous spectrum aboveμ2/2. When −1 &a

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18

Lachowicz, Miroslaw. "A class of individual-based models." BIOMATH 7, no. 1 (2018): 1804127. http://dx.doi.org/10.11145/j.biomath.2018.04.127.

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We discuss a class of mathematical models of biological systems at microscopic level - i.e. at the level of interacting individuals of a population. The class leads to partially integral stochastic semigroups- [5]. We state general conditions guaranteeing the asymptotic stability. In particular under some rather restrictive assumptions we observe that any, even non-factorized, initial probability density tends in the evolution to a factorized equilibrium probability density - [4]. We discuss possible applications of the general theory such as redistribution of individuals - [2], thermal denatu

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19

Vieni, Casey, Mark Yazer, and Jansen Seheult. "A stochastic multicompartment model of hemostasis and oxygenation during trauma resuscitation as a platform for in silico trials of transfusion." American Journal of Clinical Pathology 160, Supplement_1 (2023): S121—S122. http://dx.doi.org/10.1093/ajcp/aqad150.265.

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Abstract Uncontrolled hemorrhage accounts for up to 40% of trauma related mortality, and approximately 30% of trauma related deaths occur in the hospital within the first 1-4 hours of injury. The Advanced Trauma Life Support (ATLS) guidelines still recommend initial resuscitation with crystalloid fluid as an integral part of maintaining or restoring hemodynamic stability, but are starting to recognize the role of early resuscitation with blood products in patients with evidence of Class III and IV hemorrhage, in line with recent clinical trial and observational data. Although there is a growin

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20

Natih, Putu Geniki Lavinia. "Technical Efficiency Levels of Rural Banks (BPRs) in West Java: A Stochastic Frontier Approach." Economics and Finance in Indonesia 61, no. 3 (2015): 223. http://dx.doi.org/10.7454/efi.v61i3.513.

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There is considerable evidence from around the world to support the idea that access to formal financial services is a key factor towards achieving poverty alleviation. The government of Indonesia has placed high importance on the issue of improved access to financial services and one feels that it would be appropriate to begin the process of analyzing effective financial inclusion initiatives with the existing Bank Perkreditan Rakyat (BPR) system. BPRs have long been an integral part of Indonesia’s financial, economic, and social development. This research is focused on BPRs in West Java. In

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21

Russek, Andrzej. "On an extension of the stochastic integral." Stochastic Processes and their Applications 39, no. 1 (1991): 45–53. http://dx.doi.org/10.1016/0304-4149(91)90030-g.

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22

León, Jorge A. "Stochastic Fubini Theorem for Semimartingales in Hilbert Space." Canadian Journal of Mathematics 42, no. 5 (1990): 890–901. http://dx.doi.org/10.4153/cjm-1990-046-8.

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In this paper we will study the Fubini theorem for stochastic integrals with respect to semimartingales in Hilbert space.Let (Ω, , P) he a probability space, (X, , μ) a measure space, H and G two Hilbert spaces, L(H, G) the space of bounded linear operators from H into G, Z an H-valued semimartingale relative to a given filtration, and φ: X × R+ × Ω → L(H, G) a function such that for each t ∈ R+ the iterated integrals are well-defined (the integrals with respect to μ are Bochner integrals). It is often necessary to have sufficient conditions for the process Y1 to be a version of the process Y2

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23

Wiktorsson, Magnus. "Simulation of stochastic integrals with respect to Lévy processes of type G." Stochastic Processes and their Applications 101, no. 1 (2002): 113–25. http://dx.doi.org/10.1016/s0304-4149(02)00123-0.

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Kalpana, Rajput, Rajshreemishra, Jain D.K., and Ahmad Farooq. "A Note on Natural Transformation & Meijer's G-Function." A Note on Natural Transformation & Meijer's G-Function 10, no. 03 (2022): 2630–32. https://doi.org/10.5281/zenodo.6381907.

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The objective of this paper is to investigate natural transform of Meijer’s G-Function in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties in terms of Mittag-Leffler functions. Further, we show some applications of these natural transform in classical equations of mathematical physics, like the heat and the free electron laser equations, and in difference-differential equations governing the dynamics of generalized renewal stochastic processes.

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Ширяев, А. Н. "О принятии решений в вероятностных моделях с неопределенностью". Journal of the New Economic Association, № 4(65) (24 грудня 2024): 12–29. https://doi.org/10.31737/22212264_2024_4_12-29.

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В основе современной теории вероятностей лежит понятие «вероятностное пространство», которое позволяет определить такие понятия, как «случайная величина» и ее «математическое ожидание». Они являются объектами, в терминах которых, в частности, определяется качество выносимых решений, даются определения оптимальных решающих функций и функций полезности. В вероятностных моделях систем с неопределенностью (вероятностно- неопределенные системы) приходится иметь дело уже не с одним вероятностным пространством, а с их семейством. В этом случае привлекают такие понятия, как «сублинейные ожидания», «g-

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El-Gendy, Maysa E. I., and Ahmed M. A. El-Sayed. "Ulam stability and continuous dependence of the solution of a nonlocal stochastic-integral fractional orders stochastic differential equation." Boletim da Sociedade Paranaense de Matemática 43 (January 27, 2025). https://doi.org/10.5269/bspm.66399.

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Stochastic problems have become an indispensable tool in modeling complex systems across various disciplines, including biology, chemistry, physics, economics, finance, mechanics and several areas. In this paper, we are concerning with the nonlocal problem of the integro-fractional orders stochastic differential equation dX(t) dt = f(t,DX(t)) + g(t,B(t)), t (0, T], with the nonlocal stochastic-integral conditiom X() = X0 + Z T− 0 h(s,DX(s))dW(s),[0, T] where W is a standard Brownian motion, B is any Brownian motion and X0 is a second order random variable. The existence of solution and its con

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Jacobovic, Royi, and Michel Mandjes. "Externalities in Queues as Stochastic Processes: The Case of FCFS M/G/1." Stochastic Systems, July 24, 2023. http://dx.doi.org/10.1287/stsy.2022.0021.

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Externalities are the costs that a user of a common resource imposes on others. In the context of an FCFS M/G/1 queue, where a customer with service demand [Formula: see text] arrives when the workload level is [Formula: see text], the externality [Formula: see text] is the total waiting time that could be saved if this customer gave up on their service demand. In this work, we analyze the externalities process [Formula: see text]. It is shown that this process can be represented by an integral of a (shifted in time by v) compound Poisson process with a positive discrete jump distribution, so

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28

Sabelfeld, Karl K., and Georgy Agarkov. "Combining randomized and deterministic iterative algorithms for high accuracy solution of large linear systems and boundary integral equations." Monte Carlo Methods and Applications, March 28, 2025. https://doi.org/10.1515/mcma-2025-2008.

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Abstract This article continues the research on combined stochastic-deterministic iterative algorithms for solving large system of linear algebraic equations we developed in our previous study [K. K. Sabelfeld and G. Agarkov, Randomized vector algorithm with iterative refinement for solving boundary integral equations, Monte Carlo Methods Appl. 30 2024, 4, 375–388]. In this paper we focus on two issues: Variance reduction and extension of randomized algorithms by combining them with Krylov type iterative methods like the method of conjugate gradients, the conjugate residual method, and Craig’s

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Kremer, D. "Implicit max-stable extremal integrals." Extremes, October 22, 2020. http://dx.doi.org/10.1007/s10687-020-00388-x.

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Abstract Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function f ≥ 0. From an application point of view, one is rather interested in extreme loss events that occur relative to f than in the corresponding extreme values itself. In this context, so-called f -implicit α-Fréchet max-stable distributions arise and have been used to construct independently scattered sup-measures that possess such margins. In this paper we solve an open problem in Goldbach (2016) by developing a stochastic integral of a deterministic function g ≥ 0

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Braides, Andrea, Gianni Dal Maso, and Claude Le Bris. "A closure theorem for $\Gamma$-convergence and $H$-convergence with applications to non-periodic homogenization." Annales de l'Institut Henri Poincaré C, Analyse non linéaire, November 5, 2024. http://dx.doi.org/10.4171/aihpc/147.

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In this work we examine the stability of some classes of integrals, in particular with respect to homogenization. The prototypical case is the homogenization of quadratic energies with periodic coefficients perturbed by a term vanishing at infinity, which has recently been examined in the framework of elliptic PDEs. We use localization techniques and higher-integrability Meyers-type results to provide a closure theorem by \Gamma -convergence within a large class of integral functionals. From such a result we derive stability theorems in homogenization which comprise the case of perturbations w

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Zili, Mounir. "Stochastic Calculus with a Special Generalized Fractional Brownian Motion." International Journal of Applied Mathematics and Simulation 1, no. 1 (2024). https://doi.org/10.69717/ijams.v1.i1.96.

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This work is a first step toward developing a stochastic calculus theory with respect to the generalized fractional Brownian motion, which a recently introduced Gaussian process is extending both fractional and sub-fractional Brownian motions. A Malliavin divergence operator and a stochastic symmetric integral with respect to this process are defined, and sufficient integrability conditions are provided. Moreover, corresponding Ito formulas are established, then applied to introduce a generalized version of the fractional Black–Scholes option pricing model. MSC: 60G15, 60G22, 60H05. REFERENCES

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Gradenigo, Giacomo. "Symplectic Quantization II: Dynamics of Space–Time Quantum Fluctuations and the Cosmological Constant." Foundations of Physics 51, no. 3 (2021). http://dx.doi.org/10.1007/s10701-021-00468-3.

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AbstractThe symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor $$g_{\mu \nu }$$ g μ ν on an additional time variable, named intrinsic time at variance with the coordinate time of relativity, from which it is different. The physical meani

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Muzalevskiy, K. V. "BROADBAND REFLECTOMETRIC METHOD FOR THE MEASURING OF SOIL SURFACE MOISTURE AND ROUGHNESS." Journal of Radio Electronics 2022, no. 12 (2022). http://dx.doi.org/10.30898/1684-1719.2022.12.5.

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In this article, a numerical-analytical model of the reflection coefficient of an electromagnetic wave from a rough soil surface is proposed. Based on the created model of reflection coefficient, in the frequency range from 520 MHz to 1.26 GHz, a broadband method for the root-mean-square deviation (RMS) of heights and volumetric moisture of rough soil surface is developed. When the model of reflection coefficient creating, the field of reflected wave from the rough soil surface was presented as the sum of secondary fields from an infinite set of elementary horizontal scattering plates (with a

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Verma, Meetu. "High-resolution observations of two pores with the integral field unit (IFU) of the GREGOR Infrared Spectrograph (GRIS)." Astronomy & Astrophysics, June 28, 2024. http://dx.doi.org/10.1051/0004-6361/202347571.

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Solar pores are associated with two significant transitions in magnetohydrodynamics: the magnetic field becomes sufficiently strong to inhibit convective energy transport, and a critical change causes pores to develop a penumbra and to transform into sunspots. The goal is to compare the intricate details of the magnetic and flow fields around two solar pores, where one is part of an active region and the other is an isolated pore, with a secondary goal of demonstrating the scientific capabilities of the GREGOR Infrared Spectrograph (GRIS) integral field unit (IFU). Two pores were observed with

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Agahi, Hamzeh, Gholamreza Karamali, and Milad Yadollahzadeh. "Stochastic g-Fractional Integrals and their Bounds for Convex Stochastic Processes." Results in Mathematics 74, no. 4 (2019). http://dx.doi.org/10.1007/s00025-019-1112-x.

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Rajshreemishra, Kalpana Rajput,. "A Note on Natural Transformation & Meijer’s G-Function." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 03 (2022). http://dx.doi.org/10.47191/ijmcr/v10i3.06.

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The objective of this paper is to investigate natural transform of Meijer’s G-Function in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties in terms of Mittag-Leffler functions. Further, we show some applications of these natural transform in classical equations of mathematical physics, like the heat and the free electron laser equations, and in difference-differential equations governing the dynamics of generalized renewal stochastic processes.

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Kim, Mun-Chol, Hun O, and Ho-Jin Hwang. "Optimal stopping under g-expectation with -integrable reward process." Journal of Applied Probability, September 14, 2022, 1–12. http://dx.doi.org/10.1017/jpr.2022.35.

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Abstract In this paper we study a class of optimal stopping problems under g-expectation, that is, the cost function is described by the solution of backward stochastic differential equations (BSDEs). Primarily, we assume that the reward process is $L\exp\bigl(\mu\sqrt{2\log\!(1+L)}\bigr)$ -integrable with $\mu>\mu_0$ for some critical value $\mu_0$ . This integrability is weaker than $L^p$ -integrability for any $p>1$ , so it covers a comparatively wide class of optimal stopping problems. To reach our goal, we introduce a class of reflected backward stochastic differential equations (RB

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Han, Yi. "A support theorem for parabolic stochastic PDEs with nondegenerate Hölder diffusion coefficients." Stochastics and Partial Differential Equations: Analysis and Computations, September 27, 2023. http://dx.doi.org/10.1007/s40072-023-00312-x.

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AbstractIn this paper we work with parabolic SPDEs of the form $$\begin{aligned} \partial _t u(t,x)=\partial _x^2 u(t,x)+g(t,x,u)+\sigma (t,x,u)\dot{W}(t,x) \end{aligned}$$ ∂ t u ( t , x ) = ∂ x 2 u ( t , x ) + g ( t , x , u ) + σ ( t , x , u ) W ˙ ( t , x ) with Neumann boundary conditions, where $$x\in [0,1]$$ x ∈ [ 0 , 1 ] , $$\dot{W}(t,x)$$ W ˙ ( t , x ) is the space-time white noise on $$(t,x)\in [0,\infty )\times [0,1]$$ ( t , x ) ∈ [ 0 , ∞ ) × [ 0 , 1 ] , g is uniformly bounded, and the solution $$u\in \mathbb {R}$$ u ∈ R is real valued. The diffusion coefficient $$\sigma $$ σ is assume

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Son, Pham Ngoc, Tran Trung Duy, Phuc Quang Truong, et al. "Combining Power Allocation and Superposition Coding for an Underlay Two-way Decode-and-forward Scheme." VNU Journal of Science: Computer Science and Communication Engineering 37, no. 1 (2021). http://dx.doi.org/10.25073/2588-1086/vnucsce.253.

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In this paper, we analyze an underlay two-way decode-and-forward scheme in which secondary relays use successive interference cancellation (SIC) technology to decode data of two secondary sources sequentially, and then generate a coded signal by superposition coding (SC) technology, denoted as SIC-SC protocol. The SIC-SC protocol is designed to operate in two time slots under effects from an interference constraint of a primary receiver and residual interference of imperfect SIC processes. Transmit powers provided to carry the data are allocated dynamically according to channel powers of inter

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Nazneen, Fatema, Bakkar Siddik Abu, and Mohammed Ibrahim Abdullah. "Efficiency and Productivity of Commercial Banks: Evidence from Bangladesh." July 21, 2019. https://doi.org/10.5281/zenodo.3344973.

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<strong>Introduction</strong> Since the early 1970s, the banking sector in Bangladesh is one of the most important instruments of countries financial system. Since commercial banks is an integral part of the financial system in Bangladesh, an efficient and productive banking system strengthen the economy of the country. Therefore, all financial institutions, including commercial banks, are required to accomplish economic objectives set by the government of a country. For long-term investments and the base of economic escalation, the banking segment is the key source of funds (Schumpeter, 1934)

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