Topic
Increasing process
About: Increasing process is a research topic. Over the lifetime, 80 publications have been published within this topic receiving 2002 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, a new class of generalized backward doubly stochastic differential equations is investigated, which involves an integral with respect to an adapted continuous increasing process, and a probabilistic representation for viscosity solutions of semi-linear partial differential equations with a Neumann boundary condition is given.
Abstract: In this paper a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.
65 citations
TL;DR: In this article, the existence and uniqueness of one-dimensional stochastic differential equations driven by a Brownian motion and an increasing process was studied and it was shown that under fairly general conditions on the diffusion coefficient, if the drift coefficient is cadlag in x and has only positive jumps, then maximal and minimal strict solutions exist.
Abstract: We study questions of existence and uniqueness for one-dimensional stochastic differential equations driven by a Brownian motion and an increasing process It is shown that under fairly general conditions on the diffusion coefficient, if the drift coefficient is cadlag in x and has only positive jumps, then maximal and minimal strict solutions exist If the drift coefficient has negative jumps, then the stochastic differential equation need not have a solution on any space We give an example showing that the maximal and minimal solutions may be distinct as soon as the classical Lipschitz condition on the drift coefficient is weakened
55 citations
TL;DR: In this article, a new class of generalized backward doubly stochastic differential equations (GBDSDEs) driven by Teugels martingales associated with Levy process and the integral with respect to an adapted continuous increasing process is investigated.
32 citations
TL;DR: In this paper, a short proof of the Doob-meyer decomposition theorem is given, and several previously known arguments are included to keep the paper self-contained.
31 citations
TL;DR: In this paper, an elementary theory of a stochastic integral with respect to the Poisson process is given and applied to stochastically differential equations driven by a poisson process, as well as concrete examples.
Abstract: An elementary theory of a stochastic integral with respect to the Poisson process is given and applied to stochastic differential equations driven by a Poisson process, as well as to concrete examples. The treatment does not use the extensive machinery of the general theory of processes, except for the existence of the dual predictable projection of an integrable increasing process
30 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 3 |
| 2019 | 1 |
| 2018 | 1 |
| 2016 | 1 |
| 2014 | 2 |