<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Causality is a topic which receives much attention nowadays and it represents a prediction property in the context of possible reduction of available information in order to predict a given filtration. In this paper we define the concept of dependence between stochastic processes and between filtrations, named causal predictability, which is based on the Granger’s definition of causality. This definition extends the ones already given in the continuous time. Then, we provide some properties of the given concept.</p>
<p>Finally, we apply the concept of causal predictability to the processes of the diffusion type, more precisely, to the uniqueness of weak solutions of the stochastic differential equations.</p>
</abstract>

Causality is a topic which receives much attention nowadays and it represents a prediction property in the context of possible reduction of available information in order to predict a given filtration. In this paper we define the concept of dependence between stochastic processes and between filtrations, named causal predictability, which is based on the Granger’s definition of causality. This definition extends the ones already given in the continuous time. Then, we provide some properties of the given concept.
Finally, we apply the concept of causal predictability to the processes of the diffusion type, more precisely, to the uniqueness of weak solutions of the stochastic differential equations.

Predictability and uniqueness of weak solutions of the stochastic differential equations

Department of Probability and Mathematical Statistics

University of Belgrade, Faculty of Mathematics

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Causality is a topic which receives much attention nowadays and it represents a prediction property in the context of possible reduction of available...

Predictability and uniqueness of weak solutions of the stochastic differential equations

Published Online: Feb 04, 2023

Page range: 207 - 219

Received: Apr 07, 2022

Accepted: Sep 15, 2022

DOI: https://doi.org/10.2478/auom-2023-0011

Keywords
Filtration, causal predictability, stochastic differential equations, weak solution, weak uniqueness

© 2023 Ana Merkle, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Predictability and uniqueness of weak solutions of the stochastic differential equations

Published Online: Feb 04, 2023

Page range: 207 - 219

Received: Apr 07, 2022

Accepted: Sep 15, 2022

DOI: https://doi.org/10.2478/auom-2023-0011

KeywordsFiltration, causal predictability, stochastic differential equations, weak solution, weak uniqueness

© 2023 Ana Merkle, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Filtration, causal predictability, stochastic differential equations, weak solution, weak uniqueness