Solution of stochastic differential equations by random time change

1975 ◽  
Vol 2 (1) ◽  
pp. 90-96 ◽  
Author(s):  
Shinzo Watanabe
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Time Change ◽  
Random Time ◽  
Random Time Change

Well-posedness of Stratonovich multi-valued SDEs driven by semimartingales

2014 ◽  
Vol 14 (04) ◽  
pp. 1450005
Author(s):  
Jing Wu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Time Change ◽  
Random Time ◽  
Approximation Technique ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Random Time Change

In this paper we consider Stratonovich type multi-valued stochastic differential equations (MSDEs) driven by general semimartingales. Based on an existence and uniqueness result for MSDEs with respect to continuous semimartingales, we apply the random time change and approximation technique to prove existence and uniqueness of solutions to Stratonovich type multi-valued SDEs driven by general semimartingales with summable jumps.

A framework of BSDEs with stochastic Lipschitz coefficients

2020 ◽  
Vol 24 ◽  
pp. 739-769
Author(s):  
Hun O ◽  
Mun-Chol Kim ◽  
Chol-Kyu Pak
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Large Class ◽  
Lipschitz Condition ◽  
Time Change ◽  
Random Time ◽  
Effective Technique ◽  
Random Time Change ◽  
Monotone Coefficients ◽  
Terminal Time

In this paper, we suggest an effective technique based on random time-change for dealing with a large class of backward stochastic differential equations (BSDEs for short) with stochastic Lipschitz coefficients. By means of random time-change, we show the relation between the BSDEs with stochastic Lipschitz coefficients and the ones with bounded Lipschitz coefficients and stopping terminal time, so they are possible to be exchanged with each other from one type to another. In other words, the stochastic Lipschitz condition is not essential in the context of BSDEs with random terminal time. Using this technique, we obtain a couple of new results of BSDEs with stochastic Lipschitz (or monotone) coefficients.

Time-changing and truncating K-capacity queues from one K to another

1991 ◽  
Vol 28 (3) ◽  
pp. 647-655 ◽  
Author(s):  
Paul Glasserman ◽  
Wei-Bo Gong
Keyword(s):  
Queue Length ◽  
Sample Path ◽  
Time Change ◽  
Random Time ◽  
Random Time Change ◽  
Vacation Model

For , we obtain a K′- capacity queue from a K- capacity queue through a random time change and a truncation, provided arrivals are Poisson or service is exponential. In the case of an M/G/1/K queue, the time change erases service intervals that begin with more than K′ customers in the systems. This construction yields a straightforward sample path proof of Keilson's result on the proportionality of the ergodic queue length probabilities in M/G/1/K queues. The same approach proves a strengthened result for ‘detailed' state probabilities. It also reproduces a proportionality result for a vacation model, due to Keilson and Servi. A ‘dual' construction yields a different kind of proportionality for the G/M/1/K queue.

A simple proof of the multivariate random time change theorem for point processes

1988 ◽  
Vol 25 (01) ◽  
pp. 210-214 ◽  
Author(s):  
Timothy C. Brown ◽  
M. Gopalan Nair
Keyword(s):  
Poisson Process ◽  
Simple Proof ◽  
Point Processes ◽  
Time Change ◽  
Random Time ◽  
Random Time Change ◽  
Special Case

A simple proof of the multivariate random time change theorem of Meyer (1971) is given. This result includes Watanabe's (1964) characterization of the Poisson process; even in this special case the present proof is simpler than existing proofs.

A simple proof of the multivariate random time change theorem for point processes

1988 ◽  
Vol 25 (1) ◽  
pp. 210-214 ◽  
Author(s):  
Timothy C. Brown ◽  
M. Gopalan Nair
Keyword(s):  
Poisson Process ◽  
Simple Proof ◽  
Point Processes ◽  
Time Change ◽  
Random Time ◽  
Random Time Change ◽  
Special Case

A simple proof of the multivariate random time change theorem of Meyer (1971) is given. This result includes Watanabe's (1964) characterization of the Poisson process; even in this special case the present proof is simpler than existing proofs.

scholarly journals Random time transformation analysis of Covid19 2020

2020 ◽  
Author(s):  
Nitay Alon ◽  
Isaac Meilijson
Keyword(s):  
Parameter Estimation ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Exponential Growth ◽  
Growth Pattern ◽  
Polynomial Growth ◽  
Present Report ◽  
Random Time ◽  
Time Transformation ◽  
Simple Method

AbstractThe SIR epidemiological equations model new affected and removed cases as roughly proportional to the current number of infected cases. The present report adopts an alternative that has been considered in the literature, in which the number of new affected cases is proportional to the α ≤ 1 power of the number of infected cases. After arguing that α = 1 models exponential growth while α < 1 models polynomial growth, a simple method for parameter estimation in differential equations subject to noise, the random-time transformation RTT of Bassan, Meilijson, Marcus and Talpaz 1997, will be reviewed and compared with stochastic differential equations. Both methods are applied in an attempt to uncover the growth pattern of Covid19.

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