Stochastic Integration and Differential Equations— Physical Approach

1969 ◽  
pp. 109-129
Author(s):  
S. K. Srinivasan
Keyword(s):  
Differential Equations ◽  
Stochastic Integration ◽  
Physical Approach

Quantum stochastic integration and quantum stochastic differential equations

1994 ◽  
Vol 116 (3) ◽  
pp. 535-553 ◽  
Author(s):  
Chris Barnett ◽  
Stanisław Goldstein ◽  
Ivan Wilde
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Integrals ◽  
Explicit Solutions ◽  
Space Theory ◽  
Stochastic Integration ◽  
Uniqueness Of The Solution

AbstractQuantum stochastic integrals are constructed using the non-commutative Lp-space theory of Haagerup. The existence and uniqueness of the solution to quantum stochastic differential equations driven by quasi-Wiener noises, or noises satisfying generalized standing hypotheses, is established as is the Markov behaviour of the solution. Various examples of the theory are discussed, and quantum Ornstein-Uhlenbeck processes are obtained as explicit solutions.

scholarly journals Stochastic integration and differential equations for typical paths

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Daniel Bartl ◽  
Michael Kupper ◽  
Ariel Neufeld
Keyword(s):  
Differential Equations ◽  
Stochastic Integration

ROBUST FILTERING AND DETECTION OF AN INSURANCE MODEL

2007 ◽  
Vol 07 (01) ◽  
pp. 91-102 ◽  
Author(s):  
LAKHDAR AGGOUN
Keyword(s):  
Differential Equations ◽  
Stochastic Models ◽  
Point Processes ◽  
Risk Theory ◽  
Robust Filtering ◽  
Stochastic Integration ◽  
Competing Models ◽  
Rate Processes ◽  
The Difference ◽  
Insurance Model

Risk theory deals with stochastic models in insurance business. Usually, in such models claims are described by point processes and the amounts claimed by policy holders are sequences of random variables. The profit or loss, of the company is the difference between premiums income and the claims. We assume that we have a certain number of competing models, describing the claims and premiums rate processes. We are interested in ranking the candidate models based on their likelihood of being most appropriate for describing these processes. We compute robust dynamics for our estimates. In these new dynamics stochastic integration disappear and stochastic differential equations become ordinary differential equations.

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