Carathéodory approximate solutions for a class of perturbed reflected stochastic differential equations with irregular coefficients
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Cited by 2 publications
References 26 publications
This article investigates the Carathéodory approximation scheme for stochastic differential equations (SDEs) in the G‐Lévy process framework. In the context of the G‐Lévy process, the possibility of SDE solutions has been developed. The solution's boundedness and uniqueness have been discussed. The convergence of approximate Carathéodory solutions to the unique solution of the given SDEs has been determined. The G‐Lévy framework is used to obtain exponential estimates for solutions to SDEs. An example has been provided to validate the results.
This article investigates the Carathéodory approximation scheme for stochastic differential equations (SDEs) in the G‐Lévy process framework. In the context of the G‐Lévy process, the possibility of SDE solutions has been developed. The solution's boundedness and uniqueness have been discussed. The convergence of approximate Carathéodory solutions to the unique solution of the given SDEs has been determined. The G‐Lévy framework is used to obtain exponential estimates for solutions to SDEs. An example has been provided to validate the results.
Existence and uniqueness of solutions for perturbed stochastic differential equations with reflected boundary
In this paper, under some suitable conditions, we prove existence of a strong solution and uniqueness for the perturbed stochastic differential equations with reflected boundary (PSDERB), that is, { x ( t ) = x ( 0 ) + ∫ 0 t σ ( s , x ( s ) ) d B ( s ) + ∫ 0 t b ( s , x ( s ) ) d s + α ( t ) H ( max 0 ≤ u ≤ t x ( u ) ) + β ( t ) L t 0 ( x ) , x ( t ) ≥ 0 for all t ≥ 0 , \left\{\begin{aligned} {}x(t)&=x(0)+\int_{0}^{t}\sigma(s,x(s))\,dB(s)+\int_{0}^{t}b(s,x(s))\,ds+\alpha(t)H\bigl{(}\max_{0\leq u\leq t}x(u)\bigr{)}+\beta(t)L_{t}^{0}(x),\\ x(t)&\geq 0\quad\text{for all}\ t\geq 0,\end{aligned}\right. where 𝐻 is a continuous R-valued function, σ , b , α \sigma,b,\alpha and 𝛽 are measurable functions, L t 0 L_{t}^{0} denotes a local time at point zero for the time of the semi-martingale 𝑥.
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