An asymptotically probabilistic method for a class of partial integrodifferential equations

Alioune Coulibaly; Alioune Coulibaly

doi:10.3934/math.2025607

AIMS Mathematics

2025, Volume 10, Issue 6: 13512-13523. doi: 10.3934/math.2025607

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An asymptotically probabilistic method for a class of partial integrodifferential equations

Alioune Coulibaly ^,

Département Mathématiques, Informatique et Modélisation, UFR Sciences et Technologies Avancées, Université Amadou Mahtar Mbow, Pôle Urbain de Diamniadio - BP : 45927 Dakar NAFA VDN Dakar, Sénégal

Received: 25 February 2025 Revised: 28 May 2025 Accepted: 06 June 2025 Published: 12 June 2025
MSC : 60H30, 35K40

In this paper, we consider a nonlocal boundary condition and examine the asymptotic behavior of the solution to a family of nonlocal partial differential equations in the half-space. Our approach is fully probabilistic and builds upon the works of Huang et al. Bernoulli, 28 (2022), 1648–1674 and Diakhaby et al. Stoch. Anal. Appl., 34 (2016), 496–509. Reflected stochastic differential equations, driven by multiplicative Lévy noise and with singular coefficients, play an important role in our method.
- nonlocal PDE,
- Hamilton-Jacobi equations,
- viscosity solutions,
- Lévy noise
Citation: Alioune Coulibaly. An asymptotically probabilistic method for a class of partial integrodifferential equations[J]. AIMS Mathematics, 2025, 10(6): 13512-13523. doi: 10.3934/math.2025607

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Abstract

In this paper, we consider a nonlocal boundary condition and examine the asymptotic behavior of the solution to a family of nonlocal partial differential equations in the half-space. Our approach is fully probabilistic and builds upon the works of Huang et al. Bernoulli, 28 (2022), 1648–1674 and Diakhaby et al. Stoch. Anal. Appl., 34 (2016), 496–509. Reflected stochastic differential equations, driven by multiplicative Lévy noise and with singular coefficients, play an important role in our method.

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