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Solutions of ordinary differential equations as limits of pure jump markov processes
Abstract
In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.
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Citations
Cited by
Strong approximation theorems for density dependent Markov chains
Kurtz, T. G. (1978) · Stochastic Processes and their Applications · doi:10.1016/0304-4149(78)90020-0 · Cited by 552
Self-citationThe Relationship between Stochastic and Deterministic Models for Chemical Reactions
Kurtz, T. G. (1972) · The Journal of Chemical Physics · doi:10.1063/1.1678692 · Cited by 536
Self-citationNetworks and the Epidemiology of Infectious Disease
Danon, L., Ford, A. P., House, T., Jewell, C. P., Keeling, M. J., Roberts, G. O., Ross, J. V., & Vernon, M. C. (2011) · Interdisciplinary Perspectives on Infectious Diseases · doi:10.1155/2011/284909 · Cited by 454
The Power of Two Random Choices: A Survey of Techniques and Results
Mitzenmacher, M., Richa, A. W., & Sitaraman, R. (2001) · Combinatorial Optimization · doi:10.1007/978-1-4615-0013-1_9 · Cited by 431
Gaussian stochastic processes in physics
Fox, R. F. (1978) · Physics Reports · doi:10.1016/0370-1573(78)90145-x · Cited by 373
Metadata
- Authors
- Kurtz, T. G.
- Venue
- Journal of Applied Probability
- Publisher
- Cambridge University Press (CUP)
- Published
- 1970-04
- Volume
- 7
- Issue
- 01
- Pages
- 49-58
- ISSN
- 0021-9002 (ISSN-L)
- 1475-6072
- OpenAlex
- W2062259223
- Cited by
- 947
- References
- 0
- FWCI
- 2.21
- Type
- journal article
- Language
- en
- Open access
- closed
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- Kurtz, T. G. (1970). Solutions of ordinary differential equations as limits of pure jump markov processes. Journal of Applied Probability. https://doi.org/10.1017/s0021900200026929
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
