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Journal articles on the topic 'Affine diffusions'

Author: Grafiati

Published: 8 February 2025

Last updated: 31 July 2025

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1

Kelly, Leah, Eckhard Platen, and Michael Sørensen. "Estimation for discretely observed diffusions using transform functions." Journal of Applied Probability 41, A (2004): 99–118. http://dx.doi.org/10.1239/jap/1082552193.

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This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.

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2

Kelly, Leah, Eckhard Platen, and Michael Sørensen. "Estimation for discretely observed diffusions using transform functions." Journal of Applied Probability 41, A (2004): 99–118. http://dx.doi.org/10.1017/s0021900200112239.

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This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.

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3

Linetsky, Vadim. "On the transition densities for reflected diffusions." Advances in Applied Probability 37, no. 2 (2005): 435–60. http://dx.doi.org/10.1239/aap/1118858633.

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Diffusion models in economics, finance, queueing, mathematical biology, and electrical engineering often involve reflecting barriers. In this paper, we study the analytical representation of transition densities for reflected one-dimensional diffusions in terms of their associated Sturm-Liouville spectral expansions. In particular, we provide explicit analytical expressions for transition densities of Brownian motion with drift, the Ornstein-Uhlenbeck process, and affine (square-root) diffusion with one or two reflecting barriers. The results are easily implementable on a personal computer and

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4

Linetsky, Vadim. "On the transition densities for reflected diffusions." Advances in Applied Probability 37, no. 02 (2005): 435–60. http://dx.doi.org/10.1017/s0001867800000252.

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Diffusion models in economics, finance, queueing, mathematical biology, and electrical engineering often involve reflecting barriers. In this paper, we study the analytical representation of transition densities for reflected one-dimensional diffusions in terms of their associated Sturm-Liouville spectral expansions. In particular, we provide explicit analytical expressions for transition densities of Brownian motion with drift, the Ornstein-Uhlenbeck process, and affine (square-root) diffusion with one or two reflecting barriers. The results are easily implementable on a personal computer and

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5

Spreij, Peter, and Enno Veerman. "Affine Diffusions with Non-Canonical State Space." Stochastic Analysis and Applications 30, no. 4 (2012): 605–41. http://dx.doi.org/10.1080/07362994.2012.684322.

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6

Duffie, Darrell, Jun Pan, and Kenneth Singleton. "Transform Analysis and Asset Pricing for Affine Jump-diffusions." Econometrica 68, no. 6 (2000): 1343–76. http://dx.doi.org/10.1111/1468-0262.00164.

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7

Barletta, Andrea, and Elisa Nicolato. "Orthogonal expansions for VIX options under affine jump diffusions." Quantitative Finance 18, no. 6 (2017): 951–67. http://dx.doi.org/10.1080/14697688.2017.1371322.

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8

CHU, CHI CHIU, and YUE KUEN KWOK. "VALUATION OF GUARANTEED ANNUITY OPTIONS IN AFFINE TERM STRUCTURE MODELS." International Journal of Theoretical and Applied Finance 10, no. 02 (2007): 363–87. http://dx.doi.org/10.1142/s0219024907004160.

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We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computati

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9

Ahlip, Rehez, Laurence A. F. Park, Ante Prodan, and Stephen Weissenhofer. "Forward start options under Heston affine jump-diffusions and stochastic interest rate." International Journal of Financial Engineering 08, no. 01 (2021): 2150005. http://dx.doi.org/10.1142/s2424786321500055.

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This paper presents a generalization of forward start options under jump diffusion framework of Duffie et al. [Duffie, D, J Pan and K Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343–1376.]. We assume, in addition, the short-term rate is governed by the CIR dynamics introduced in Cox et al. [Cox, JC, JE Ingersoll and SA Ross (1985). A theory of term structure of interest rates, Econometrica 53, 385–408.]. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to b

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10

Bolyog, Beáta, and Gyula Pap. "On conditional least squares estimation for affine diffusions based on continuous time observations." Statistical Inference for Stochastic Processes 22, no. 1 (2018): 41–75. http://dx.doi.org/10.1007/s11203-018-9174-z.

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11

Jena, Rudra P., Kyoung-Kuk Kim, and Hao Xing. "Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions." Stochastic Processes and their Applications 122, no. 8 (2012): 2961–93. http://dx.doi.org/10.1016/j.spa.2012.05.007.

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12

Lu, Shan. "Monte Carlo analysis of methods for extracting risk‐neutral densities with affine jump diffusions." Journal of Futures Markets 39, no. 12 (2019): 1587–612. http://dx.doi.org/10.1002/fut.22049.

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13

Meesa, Rattiya, Ratinan Boonklurb, and Phiraphat Sutthimat. "On the Transition Density of the Time-Inhomogeneous 3/2 Model: A Unified Approach for Models Related to Squared Bessel Process." Mathematics 13, no. 12 (2025): 1948. https://doi.org/10.3390/math13121948.

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We derive an infinite-series representation for the transition probability density function (PDF) of the time-inhomogeneous 3/2 model, expressing all coefficients in terms of Bell-polynomial and generalized Laguerre-polynomial formulas. From this series, we obtain explicit expressions for all conditional moments of the variance process, recovering the familiar time-homogeneous formulas when parameters are constant. Numerical experiments illustrate that both the density and moment series converge rapidly, and the resulting distributions agree with high-precision Monte Carlo simulations. Finally

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14

da Silva, Allan Jonathan, and Jack Baczynski. "Discretely Distributed Scheduled Jumps and Interest Rate Derivatives: Pricing in the Context of Central Bank Actions." Economies 12, no. 3 (2024): 73. http://dx.doi.org/10.3390/economies12030073.

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Interest rate dynamics are influenced by various economic factors, and central bank meetings play a crucial role concerning this subject matter. This study introduces a novel approach to modeling interest rates, focusing on the impact of central banks’ scheduled interventions and their implications for pricing bonds and path-dependent derivatives. We utilize a modified Skellam probability distribution to address the discrete nature of scheduled interest rate jumps and combine them with affine jump-diffusions (AJDs) in order to realistically represent interest rates. We name this class the AJD–

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15

Kaeck, Andreas, and Carol Alexander. "Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions." Journal of Banking & Finance 36, no. 11 (2012): 3110–21. http://dx.doi.org/10.1016/j.jbankfin.2012.07.012.

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16

Detemple, Jerome, Marcel Rindisbacher, and Scott Robertson. "Dynamic Noisy Rational Expectations Equilibrium With Insider Information." Econometrica 88, no. 6 (2020): 2697–737. http://dx.doi.org/10.3982/ecta17038.

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We study equilibria in multi‐asset and multi‐agent continuous‐time economies with asymmetric information and bounded rational noise traders. We establish the existence of two equilibria. First, a full communication equilibrium where the informed agents' signal is disclosed to the market and static policies are optimal. Second, a partial communication equilibrium where the signal disclosed is affine in the informed and noise traders' signals, and dynamic policies are optimal. Here, information asymmetry creates demand for two public funds, as well as a dark pool where private information trades

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17

Song, Jiao, Jiang-Lun Wu, and Fangzhou Huang. "First jump time in simulation of sampling trajectories of affine jump-diffusions driven by \begin{document}$ \alpha $\end{document}-stable white noise." Communications on Pure & Applied Analysis 19, no. 8 (2020): 4127–42. http://dx.doi.org/10.3934/cpaa.2020184.

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18

DAUMAIL, LAURENT, and PATRICK FLORCHINGER. "A CONSTRUCTIVE EXTENSION OF ARTSTEIN'S THEOREM TO THE STOCHASTIC CONTEXT." Stochastics and Dynamics 02, no. 02 (2002): 251–63. http://dx.doi.org/10.1142/s0219493702000418.

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The aim of this paper is to extend Artstein's theorem on the stabilization of affine in the control nonlinear deterministic systems to nonlinear stochastic differential systems when both the drift and the diffusion terms are affine in the control. We prove that the existence of a smooth control Lyapunov function implies smooth stabilizability.

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19

Jin, Danqi, Jie Chen, Cedric Richard, Jingdong Chen, and Ali H. Sayed. "Affine Combination of Diffusion Strategies Over Networks." IEEE Transactions on Signal Processing 68 (2020): 2087–104. http://dx.doi.org/10.1109/tsp.2020.2975346.

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20

Glasserman, Paul, and Kyoung-Kuk Kim. "Saddlepoint approximations for affine jump-diffusion models." Journal of Economic Dynamics and Control 33, no. 1 (2009): 15–36. http://dx.doi.org/10.1016/j.jedc.2008.04.007.

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21

Behjoo, Hamidreza, and Michael Chertkov. "U-Turn Diffusion." Entropy 27, no. 4 (2025): 343. https://doi.org/10.3390/e27040343.

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We investigate diffusion models generating synthetic samples from the probability distribution represented by the ground truth (GT) samples. We focus on how GT sample information is encoded in the score function (SF), computed (not simulated) from the Wiener–Ito linear forward process in the artificial time t∈[0→∞], and then used as a nonlinear drift in the simulated Wiener–Ito reverse process with t∈[∞→0]. We propose U-Turn diffusion, an augmentation of a pre-trained diffusion model, which shortens the forward and reverse processes to t∈[0→Tu] and t∈[Tu→0]. The U-Turn reverse process is initi

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22

Hyoseok, Lee, Kyeong Seon Kim, Kwon Byung-Ki, and Tae-Hyun Oh. "Zero-shot Depth Completion via Test-time Alignment with Affine-invariant Depth Prior." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 4 (2025): 3877–85. https://doi.org/10.1609/aaai.v39i4.32405.

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Depth completion, predicting dense depth maps from sparse depth measurements, is an ill-posed problem requiring prior knowledge. Recent methods adopt learning-based approaches to implicitly capture priors, but the priors primarily fit in-domain data and do not generalize well to out-of-domain scenarios. To address this, we propose a zero-shot depth completion method composed of an affine-invariant depth diffusion model and test-time alignment. We use pre-trained depth diffusion models as depth prior knowledge, which implicitly understand how to fill in depth for scenes. Our approach aligns the

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23

Hao, Lei, Yali Huang, Yuehua Gao, Xiaoxi Chen, and Peiguang Wang. "Nonrigid Registration of Prostate Diffusion-Weighted MRI." Journal of Healthcare Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/9296354.

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Motion and deformation are common in prostate diffusion-weighted magnetic resonance imaging (DWI) during acquisition. These misalignments lead to errors in estimating an apparent diffusion coefficient (ADC) map fitted with DWI. To address this problem, we propose an image registration algorithm to align the prostate DWI and improve ADC map. First, we apply affine transformation to DWI to correct intraslice motions. Then, nonrigid registration based on free-form deformation (FFD) is used to compensate for intraimage deformations. To evaluate the influence of the proposed algorithm on ADC values

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24

Ignatieva, Katja, and Patrick Wong. "Modelling high frequency crude oil dynamics using affine and non-affine jump–diffusion models." Energy Economics 108 (April 2022): 105873. http://dx.doi.org/10.1016/j.eneco.2022.105873.

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25

Kant, Rama. "Diffusion-Limited Reaction Rates on Self-Affine Fractals." Journal of Physical Chemistry B 101, no. 19 (1997): 3781–87. http://dx.doi.org/10.1021/jp963141p.

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26

Li, Lingfei, Rafael Mendoza-Arriaga, and Daniel Mitchell. "Analytical representations for the basic affine jump diffusion." Operations Research Letters 44, no. 1 (2016): 121–28. http://dx.doi.org/10.1016/j.orl.2015.12.003.

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27

Filipović, Damir, Eberhard Mayerhofer, and Paul Schneider. "Density approximations for multivariate affine jump-diffusion processes." Journal of Econometrics 176, no. 2 (2013): 93–111. http://dx.doi.org/10.1016/j.jeconom.2012.12.003.

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28

Yoo, J. W., I. S. Song, J. W. Shin, and P. G. Park. "A variable step-size diffusion affine projection algorithm." International Journal of Communication Systems 29, no. 5 (2015): 1012–25. http://dx.doi.org/10.1002/dac.3015.

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29

Adithya B. and Santhi G. "A DNA Sequencing Medical Image Encryption System (DMIES) Using Chaos Map and Knight's Travel Map." International Journal of Reliable and Quality E-Healthcare 11, no. 4 (2022): 1–22. http://dx.doi.org/10.4018/ijrqeh.308803.

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This research aims to devise a method of encrypting medical images based on chaos map, Knight's travel map, affine transformation, and DNA cryptography to prevent attackers from accessing the data. The proposed DMIES cryptographic system performs the chaos intertwining logistic map diffusion and confusion process on chosen pixels of medical images. The DNA structure of the medical image has generated using all eight DNA encoding rules that are dependent on the pixel positions in the medical image. Knight's travel map is decomposed, which helps to prevent tampering and certification after the d

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30

Friesen, Martin, Peng Jin, Jonas Kremer, and Barbara Rüdiger. "Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices." Advances in Applied Probability 52, no. 3 (2020): 825–54. http://dx.doi.org/10.1017/apr.2020.21.

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AbstractThis article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite $d\times d$ matrices. In particular, for conservative and subcritical affine processes we show that a finite $\log$ -moment of the state-independent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: first, in a specific metric induced by the Laplace transform, and second, in the Wasserstein distance under a first moment assumption

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31

Li, Tianyou, Sipei Zhao, Kai Chen, and Jing Lu. "A diffusion filtered-x affine projection algorithm for distributed active noise control." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 268, no. 5 (2023): 3050–57. http://dx.doi.org/10.3397/in_2023_0441.

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The well-known Filtered-x Affine Projection (FxAP) algorithm is usually deemed a better choice than the conventional Filtered-x Least-Mean-Square (FxLMS) algorithm when faster convergence speed is desired in active noise control applications. However, the improvement of its convergence performance is obtained at the expense of increased computational complexity. It is usually unrealistic to regulate multichannel ANC systems using the centralized AP algorithm. Recently, distributed diffusion adaptation schemes over acoustic sensor and actuator networks have been introduced to multichannel ANC s

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32

Gapeev, Pavel V., and Yavor I. Stoev. "On the construction of non-affine jump-diffusion models." Stochastic Analysis and Applications 35, no. 5 (2017): 900–918. http://dx.doi.org/10.1080/07362994.2017.1333008.

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33

Kang, Wanmo, and Chulmin Kang. "Large deviations for affine diffusion processes onR+m×Rn." Stochastic Processes and their Applications 124, no. 6 (2014): 2188–227. http://dx.doi.org/10.1016/j.spa.2014.02.002.

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34

Sharifi-Viand, Ahmad, Mohammad Ghasem Mahjani, Reza Moshrefi, and Majid Jafarian. "Diffusion through the self-affine surface of polypyrrole film." Vacuum 114 (April 2015): 17–20. http://dx.doi.org/10.1016/j.vacuum.2014.12.030.

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35

Glasserman, Paul, and Kyoung-Kuk Kim. "MOMENT EXPLOSIONS AND STATIONARY DISTRIBUTIONS IN AFFINE DIFFUSION MODELS." Mathematical Finance 20, no. 1 (2010): 1–33. http://dx.doi.org/10.1111/j.1467-9965.2009.00387.x.

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36

Hegger, Rainer, and Peter Grassberger. "Is Diffusion Limited Aggregation Locally Isotropic or Self-Affine?" Physical Review Letters 73, no. 12 (1994): 1672–74. http://dx.doi.org/10.1103/physrevlett.73.1672.

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37

Modalavalasa, Sowjanya, Upendra Kumar Sahoo, and Ajit Kumar Sahoo. "Diffusion minimum Wilcoxon affine projection algorithm over distributed networks." Digital Signal Processing 109 (February 2021): 102918. http://dx.doi.org/10.1016/j.dsp.2020.102918.

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38

Tappe, Stefan. "Existence of affine realizations for Lévy term structure models." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2147 (2012): 3685–704. http://dx.doi.org/10.1098/rspa.2012.0089.

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We investigate the existence of affine realizations for term structure models driven by Lévy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special cases, we study constant direction volatilities and the existence of short-rate realizations.

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39

Claudia, Peerez Ruisanchez. "A NEW ALGORITHM TO CONSTRUCT S-BOXES WITH HIGH DIFFUSION." International Journal of Soft Computing, Mathematics and Control (IJSCMC) 4, no. 3 (2022): 10. https://doi.org/10.5281/zenodo.6786588.

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In this paper is proposed a new algorithm to construct S-Boxes over GF(28) with Branch Number value at least 3. This is an important property that guarantees a high diusion in the S-Box [12]. Also are introduced some defnition and properties that show the be- havior of S-Boxes under the composition with affine functions. Finally is presented a comparision between this algorithm and the method pro-posed by Tavares [12]

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40

Claudia, Peerez Ruisanchez. "A NEW ALGORITHM TO CONSTRUCT S-BOXES WITH HIGH DIFFUSION." International Journal of Soft Computing, Mathematics and Control (IJSCMC) 4, no. 3 (2015): 1 to 10. https://doi.org/10.5281/zenodo.3653528.

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In this paper is proposed a new algorithm to construct S-Boxes over GF(28) with Branch Number value at least 3. This is an important property that guarantees a high diusion in the S-Box [12]. Also are introduced some defnition and properties that show the be- havior of S-Boxes under the composition with affine functions. Finally is presented a comparision between this algorithm and the method pro-posed by Tavares [12].

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41

Florchinger, Patrick. "A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions." Control and Cybernetics 51, no. 1 (2022): 21–29. http://dx.doi.org/10.2478/candc-2022-0002.

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Abstract The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic differential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic– Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).

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42

Avram, Florin, and Miguel Usabel. "The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model." ASTIN Bulletin 38, no. 2 (2004): 461–81. http://dx.doi.org/10.1017/s0515036100015257.

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We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004).

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43

Gourieroux, C. "A Classification of Two-Factor Affine Diffusion Term Structure Models." Journal of Financial Econometrics 4, no. 1 (2005): 31–52. http://dx.doi.org/10.1093/jjfinec/nbj003.

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44

Nunes, João Pedro Vidal, and Tiago Ramalho Viegas Alcaria. "Valuation of forward start options under affine jump-diffusion models." Quantitative Finance 16, no. 5 (2015): 727–47. http://dx.doi.org/10.1080/14697688.2015.1049200.

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45

Fernandez-Bes, Jesus, Luis A. Azpicueta-Ruiz, Jerónimo Arenas-García, and Magno T. M. Silva. "Distributed estimation in diffusion networks using affine least-squares combiners." Digital Signal Processing 36 (January 2015): 1–14. http://dx.doi.org/10.1016/j.dsp.2014.09.004.

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46

Yun, Jaeho. "Out-of-sample density forecasts with affine jump diffusion models." Journal of Banking & Finance 47 (October 2014): 74–87. http://dx.doi.org/10.1016/j.jbankfin.2014.06.024.

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47

Kengnou Telem, Adélaïde Nicole, Cyrille Feudjio, Balamurali Ramakrishnan, Hilaire Bertrand Fotsin, and Karthikeyan Rajagopal. "A Simple Image Encryption Based on Binary Image Affine Transformation and Zigzag Process." Complexity 2022 (January 7, 2022): 1–22. http://dx.doi.org/10.1155/2022/3865820.

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In this paper, we propose a new and simple method for image encryption. It uses an external secret key of 128 bits long and an internal secret key. The novelties of the proposed encryption process are the methods used to extract an internal key to apply the zigzag process, affine transformation, and substitution-diffusion process. Initially, an original gray-scale image is converted into binary images. An internal secret key is extracted from binary images. The two keys are combined to compute the substitution-diffusion keys. The zigzag process is firstly applied on each binary image. Using an

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48

FRAME, SAMUEL J., and CYRUS A. RAMEZANI. "BAYESIAN ESTIMATION OF ASYMMETRIC JUMP-DIFFUSION PROCESSES." Annals of Financial Economics 09, no. 03 (2014): 1450008. http://dx.doi.org/10.1142/s2010495214500080.

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The hypothesis that asset returns are normally distributed has been widely rejected. The literature has shown that empirical asset returns are highly skewed and leptokurtic. The affine jump-diffusion (AJD) model improves upon the normal specification by adding a jump component to the price process. Two important extensions proposed by Ramezani and Zeng (1998) and Kou (2002) further improve the AJD specification by having two jump components in the price process, resulting in the asymmetric affine jump-diffusion (AAJD) specification. The AAJD specification allows the probability distribution of

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49

Avram, Florin, and Miguel Usabel. "The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model." ASTIN Bulletin 38, no. 02 (2008): 461–81. http://dx.doi.org/10.2143/ast.38.2.2033350.

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We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk &amp; Green (2004).

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50

Wu, Qi, Mingyan Han, Ting Jiang, et al. "Realistic Noise Synthesis with Diffusion Models." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 8 (2025): 8432–40. https://doi.org/10.1609/aaai.v39i8.32910.

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Deep denoising models require extensive real-world training data, which is challenging to acquire. Current noise synthesis techniques struggle to accurately model complex noise distributions. We propose a novel Realistic Noise Synthesis Diffusor (RNSD) method using diffusion models to address these challenges. By encoding camera settings into a time-aware camera-conditioned affine modulation (TCCAM), RNSD generates more realistic noise distributions under various camera conditions. Additionally, RNSD integrates a multi-scale content-aware module (MCAM), enabling the generation of structured no

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